CN113534040B - Coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes - Google Patents

Coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes Download PDF

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CN113534040B
CN113534040B CN202110599238.0A CN202110599238A CN113534040B CN 113534040 B CN113534040 B CN 113534040B CN 202110599238 A CN202110599238 A CN 202110599238A CN 113534040 B CN113534040 B CN 113534040B
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doa
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CN113534040A (en
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沈明威
胥翔竣
蒋意扬
邱存银
俞帆
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Hohai University HHU
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F18/24—Classification techniques
    • G06F18/241—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
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    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes, which comprises the following steps: step S1: for the received signal Y c The unitary transformation realizes real number domain transformation and signal decoherence processing, so that a received signal Y after the unitary transformation is obtained; step S2: singular value decomposition is performed by using the received signal Y after unitary transformation to obtain Y sv S and S sv Constructing a weighting vector w by combining with a MUSIC algorithm; step S3: solving for a super-parameter alpha by unitary transformation of a parameter matrix of an overcomplete dictionary constructed from second order steering vectors in combination with weighted sparse Bayesian inference (OGSBI) 0 Alpha and offset beta, and outputs DOA estimated valueSimulation experiment results show that: compared with the OGSBI algorithm, under the condition of a coherent information source, the estimation accuracy can be improved by about 50 percent, and the operation efficiency can be improved by about 60 percent.

Description

Coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes
Technical Field
The invention belongs to the field of radar signal processing, and particularly relates to a coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes.
Background
Direction of arrival (Direction Of Arrival, DOA) estimation is a fundamental problem in array signal processing and is one of the important tasks in many fields such as radar and sonar. In the development of the DOA estimation technology, many algorithms have been proposed successively, including a conventional DOA estimation algorithm (Capon algorithm, forward prediction algorithm, maximum entropy algorithm, minimum modulus algorithm, etc.), a subspace-based algorithm, and maximum likelihood estimation. The estimation accuracy of the subspace algorithm is completely dependent on whether the signal subspace and the noise subspace can be correctly represented, and the estimation performance of the method can be greatly reduced under the conditions of reduced snapshot number, reduced signal-to-noise ratio, correlation among target signals and the like.
With the rise of Compressed Sensing (CS) theory, researchers apply sparse representation theory to DOA estimation for sparsity of airspace and propose a number of algorithms. Of these, the most representative algorithm is the L1-SVD algorithm. However, the algorithm is that under the premise that the target angle of the signal source is just on the observation matrix, when deviation exists, namely the off-grid problem, the estimation performance is reduced.
In order to reduce errors caused by grid offset, scholars have conducted a great deal of research on the off-grid scene, and in recent years, a DOA estimation method for the off-grid problem has been proposed successively. Among them, an off-grid sparse Bayesian inference (OGSBI) algorithm proposed by Yang et al based on Bayesian ideas in the literature is representative, and the algorithm realizes high-precision DOA estimation under the condition of coarse grid. Zhang et al construct a priori weight vector of the source by combining with the MUSIC algorithm on the basis of the OGSBI algorithm, and propose a weighted sparse Bayesian (OGSBI) algorithm. Compared with the OGSBI algorithm, the OGSBI algorithm improves the convergence speed and the estimation accuracy during iteration. However, when the OGWSBI algorithm estimates a coherent source, due to the limitation of the MUSIC algorithm, the doc estimation is missed in the spatial spectrum, so that the place where the source exists cannot be weighted effectively, and the estimation accuracy of the parameters is reduced. Thus, new weighting coefficients need to be constructed to provide the iteration with a correct a priori information. In addition, in the Taylor expansion of the guide vector, the loss of the higher-order term can cause the reduction of the parameter estimation precision, so that the higher-order term needs to be added, and the estimation precision is further improved.
Disclosure of Invention
The invention provides a coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes, which aims to solve the problem that the DOA estimation precision is not high when a high-order term is deleted in the Taylor expansion of a guide vector and a weighted sparse Bayes algorithm is applied to a coherent source. On the basis of the OGSBI algorithm, the algorithm firstly expands the guide vector to the second-order Taylor expansion in order to reduce the model error caused by the first-order Taylor expansion of the guide vector; then, the unitary transformation is utilized to carry out decorrelation processing on the received signals, restore the rank of the covariance matrix, and convert the estimation model from a complex domain to a real number domain, thereby improving the estimation precision and the operation efficiency of the algorithm.
The invention adopts the following technical scheme to realize the aim:
a coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes is used for the following models: the received signal isThe sparse model expression is Y c =Φ (β) s+n, where +.>Is a signal source, beta is an angle deviation amount, +.>Representing noise, wherein M is the number of array elements, N is the number of grid divisions, T is the number of snapshots, K is the number of signal sources, and phi is an overcomplete dictionary formed by guide vectors;
the DOA estimation method comprises the following steps:
step S1: for the received signal Y c Performing unitary transformation real number domain conversion and signal decorrelation processing, so as to obtain a received signal Y after unitary transformation;
step S2: decomposing Y singular values of the received signal after unitary transformation to obtain Y sv S and S sv Constructing a weighting vector w by combining with a MUSIC algorithm;
step S3: solving super-parameter alpha by unitary transformation of parameter matrix of overcomplete dictionary constructed by second-order guide vector and combining weighted sparse Bayes inference 0 Alpha and offset beta, and outputs DOA estimated value
Further, step S3 includes the steps of:
step S31: an overcomplete dictionary is constructed by using a real source arrival angle guide vector of second-order Taylor expansion:
wherein ,Ac For an observation matrix: is distributed in [0, pi ]]The space angle on the grid is used for dispersing sampling values, and N is the grid dividing number; the steering vector for the second order taylor expansion is Is the angle theta with the real signal k Nearest grid value, +.>Is a (theta) is->First derivative of the place->Is a (theta) is->Second derivative of the location, by->Composed ofThe matrix is-> Matrix of components->
Step S32: for A in an overcomplete dictionary c 、B c C (C) c Performing unitary transformation to obtain overcomplete dictionary after unitary transformation
Step S33: by usingΛ＝diag(α)、p(α n )＝Γ(α|1,w n ρ) is a user-selected parameter and a signal source S sv Posterior probability distribution ∈> The mean and variance μ (t) =α of the signal are obtained 0 ∑Φ H y sv (t),t＝1,....K，∑＝(α 0 Φ H Φ+Λ -1 ) -1 Updating a mean μ (t) and a variance Σ of a signal using an overcomplete dictionary Φ after unitary transformation, and updating a super parameter α based on the mean μ (t) and the variance Σ of the signal 0 Alpha and offset beta; judging whether the maximum iteration number i is reached max or ||αi+1 -α i || 2 /||α i 2 And if not, updating the over-complete dictionary phi by using the updated offset beta, and continuing to update the mean mu (t) and the variance sigma of the signals by using the updated over-complete dictionary phiThereby updating the super parameter alpha 0 Alpha and offset beta; if one or two conditions are satisfied, ending the iteration and outputting DOA estimate +.>
Further, updated superparameter alpha 0 Alpha is respectively as follows:
wherein μ= [ μ (1),. Mu.μ (K)]＝α 0 ∑Φ H Y sv ， ρ＝ρ/K，/>b,c→0。
Further, the updated offset β is:
wherein ,
further, step S1 includes the steps of:
step S11: for the received signal Y c Constructing an augmentation matrix to form a central hermite matrix:
wherein ,Yc * Is Y c Is used for the complex conjugate of (a),
step S12: to the center Hermite matrix Y aug Unitary transformation processing:wherein Y represents Y aug After unitary transformation, transforming from complex domain to matrix of real number domain, U is unitary matrix;
when M is even, U M Can be expressed as:
wherein I is an identity matrix of M/2 xM/2, J is an exchange matrix of M/2 xM/2, the auxiliary diagonal line is 1, and the other elements are 0;
when M is odd number, U M Can be expressed as:
wherein the dimension of I and J is (M-1)/2;
similarly, U 2T Is a 2T dimensional unitary matrix.
Further, in step S32, a in the overcomplete dictionary is set c 、B c C (C) c A, B and C for unitary transformation are as follows:
further, step S2 includes the steps of:
singular value decomposition of the unitary transformed received signal Y, i.e. y=u s ∑ s V s T +U e ∑ e V e T Obtaining a signal subspace U s Noise subspace U e The method comprises the steps of carrying out a first treatment on the surface of the Order the Obtaining Y for the real signal source sv 、S sv ；
The inverted MUSIC spatial spectrum formula is:weight w= [ w ] 1 ,…,w N ] T And simultaneously normalizing the weight values to obtain a weight vector w: w=w/min (w).
The beneficial effects are that: carrying out decorrelation processing on the received signals by unitary transformation, and recovering the rank of a covariance matrix; meanwhile, in order to reduce model errors caused by first-order Taylor expansion of the guide vectors, the guide vectors are expanded to second-order Taylor expansion, and unitary transformation is carried out on an overcomplete dictionary formed by the guide vectors, so that a received signal sparse model Y is realized c The DOA algorithm has the characteristics of high estimation precision and high operation efficiency.
Drawings
FIG. 1 is a flow chart of a weighted second order sparse Bayesian based coherent source-off-grid DOA estimation method (IOGWSBI) in accordance with an embodiment of the present invention;
FIG. 2 is a cross-sectional view of the OGSBI algorithm for angle estimation under coherent and incoherent sources under the steering vector first-order Taylor expansion model condition;
FIG. 3 is a cross-sectional view of coherent source angle estimation of MUSIC algorithm before and after unitary transformation;
FIG. 4 is a cross-sectional view of the OGSBI algorithm and the coherent source angle estimation of the IOGWSBI;
FIG. 5 is a graph of the root mean square error versus signal to noise ratio for DOA estimation of the OGSBI algorithm and the IOGWSBI algorithm;
FIG. 6 is a graph of root mean square error versus snapshot count for DOA estimation of the OGSBI algorithm and the IOGWSBI algorithm;
FIG. 7 is a graph of OGSBI algorithm and IOGWSBI algorithm runtime versus signal-to-noise ratio.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
As shown in fig. 1, a coherent source-off-grid DOA estimation method based on weighted second-order sparse bayes is used for the following models: let K narrowband far-field signals be at an angle [ theta ] 1 ,θ 2 ,...θ K ] T Incident on a uniform linear array of M omni-directional receive array elements. The wavelength of the incident signal is lambda, and the distance between adjacent array elements is d=lambda/2.Is distributed in [0, pi ]]The space angle on the grid is used for dispersing sampling values, and N is the grid division number. When the off-grid condition occurs, the angle theta of the incident signal is due to k Does not fall completely on the grid of the observation matrix and therefore has an offset β from the angle on the observation matrix. The received signal is +.>The sparse model expression is Y c =Φ (β) s+n, where +.>Is the signal source->Representing noise, wherein M is the number of array elements, N is the number of grid divisions, T is the number of snapshots, K is the number of signal sources, and phi is an overcomplete dictionary formed by guide vectors; in the prior art, a first-order Taylor series approximation is adopted for a general guide vector;
the DOA estimation method comprises the following steps:
step S1: for the received signal Y c Performing unitary transformation real number domain conversion and signal decorrelation processing, so as to obtain a received signal Y after unitary transformation;
in step S1, a signal Y is received c The offset beta at this time takes a value of 0 when the unitary transformation is performed, and the specific unitary transformation process is as follows:
step S11: for the received signal Y c Constructing an augmentation matrix to form a central hermite matrix:
wherein ,Yc * Is Y c Is used for the complex conjugate of (a),
step S12: to the center Hermite matrix Y aug Unitary transformation processing:wherein Y represents Y aug After unitary transformation, transforming from complex domain to matrix of real number domain, U is unitary matrix;
when M is even, U M Can be expressed as:wherein I is an identity matrix of M/2 xM/2, J is an exchange matrix of M/2 xM/2, the auxiliary diagonal line is 1, and the other elements are 0;
when M is odd number, U M Can be expressed as:
wherein, the dimension of I and J is (M-1)/2, I is the identity matrix of M/2 xM/2, J is the exchange matrix of M/2 xM/2, the minor diagonal is 1, and the other elements are 0.
Similarly, U 2T Is a 2T dimensional unitary matrix.
Since unitary transformation can also recover the rank of the covariance matrix of the received signal, the rank is equal to the number K of signal sources, that is, rank (R) =k, so as to realize decoherence performance.
Step S2: decomposing Y singular values of the received signal after unitary transformation to obtain Y sv S and S sv Constructing a weighting vector w by combining with a MUSIC algorithm; the method comprises the steps of carrying out a first treatment on the surface of the
The method comprises the following specific steps: singular value decomposition of the unitary transformed received signal Y, i.e. y=u s ∑ s V s T +U e ∑ e V e T Obtaining a signal subspace U s Noise subspace U e The method comprises the steps of carrying out a first treatment on the surface of the Order the Obtaining Y for the real signal source sv 、S sv ；
The inverted MUSIC spatial spectrum formula is:weight w= [ w ] 1 ,…,w N ] T And simultaneously normalizing the weight values to obtain a weight vector w: w=w/min (w).
Step S3: solving super-parameter alpha by unitary transformation of parameter matrix of overcomplete dictionary constructed by second-order guide vector and combining weighted sparse Bayes inference 0 Alpha and offset beta, and outputs DOA estimated valueStep S3 comprises the steps of:
step S31: an overcomplete dictionary is constructed by using a real source arrival angle guide vector of second-order Taylor expansion:
wherein ,Ac For an observation matrix: is distributed in [0, pi ]]The space angle on the grid is used for dispersing sampling values, and N is the grid dividing number; the steering vector for the second order taylor expansion is Is the angle theta with the real signal k Nearest grid value, +.>Is a (theta) is->First derivative of the place->Is a (theta) is->Second derivative of the location, by->The matrix is-> Matrix of components->
Step S32: for A in an overcomplete dictionary c 、B c C (C) c Performing unitary transformation to obtain overcomplete dictionary after unitary transformation
For a uniform linear array, the steering vector satisfies the center hermitian property, step S32 for a in the overcomplete dictionary c 、B c C (C) c A, B and C for unitary transformation are as follows:
the whole estimation model is converted from a complex domain to a real domain by unitary transformation of the received signals and the observation matrix, so that the calculated amount is effectively reduced.
Step S33: by usingΛ＝diag(α)、p(α n )＝Γ(α|1,w n ρ) is a user-selected parameter and a signal source S sv Posterior probability distribution ∈> The mean and variance μ (t) =α of the signal are obtained 0 ∑Φ H y sv (t),t＝1,....K，∑＝(α 0 Φ H Φ+Λ -1 ) -1 Updating a mean μ (t) and a variance Σ of a signal using an overcomplete dictionary Φ after unitary transformation, and updating a super parameter α based on the mean μ (t) and the variance Σ of the signal 0 Alpha and offset beta; judging whether the maximum iteration number i is reached max or ||αi+1 -α i || 2 /||α i || 2 And if not, updating the unitary transformed overcomplete dictionary phi by using the updated offset beta, and continuously updating the mean mu (t) and the variance sigma of the signals by using the updated overcomplete dictionary phi so as to update the superparameter alpha 0 Alpha and offset beta; if one or two conditions are satisfied, ending the iteration and outputting DOA estimate +.>
In step S33, the weighting vector w is obtained in step S2 and then fused into a sparse bayesian framework. For signal distribution according to the sparse bayesian algorithm, it is assumed that it satisfies:
wherein ,ssv (t) represents S sv T th column of (2), diagonal momentThe matrix Λ=diag (α), α= [ α 1 ,...,α N ] T ，α n Controlling sparsity of signal sources, i.e. alpha in the direction in which only the source is present n Is a non-zero number. Adding the weight vector to its probability density hypothesis, assuming that it satisfies the Gamma distribution: p (a) n )＝Γ(a|1,w n ρ). Wherein Γ (·) is a Gamma function, ρ is a user selectivity parameter, w n Is the nth weight coefficient. From a signal source S sv Posterior probability distribution of (2)The mean and covariance of the obtained signal satisfy:
μ(t)＝α 0 ∑Φ H y sv (t),t＝1,....K (2)
∑＝(α 0 Φ H Φ+Λ -1 ) -1 (3)
updated superparameter alpha 0 Alpha is respectively as follows:
in the formula (4) and the formula (5), μ= [ μ (1),. Mu.k]＝α 0 ∑Φ H Y sv ， ρ＝ρ/K，/>b,c→0。
The method for solving the angle deviation beta is to make E { lovp (Y) sv |S sv ,α 0 Beta) p (beta) is maximized to maximize the following formulaMinimum:
the updated formula of the offset β is calculated:
wherein ,
to further simplify the offset calculation, letIn order to transform the matrix,is the N x 1 column vector of the ith behavior 1, the other behavior 0. Beta -k Representing the part of the offset beta other than the kth element, let +.>Beta pair new And (3) performing transformation to obtain:
wherein ,d1 is beta T P 1 Beta intermediate and beta k Irrelevant sections. Similarly, the following is true:
V 1 T β＝(V 1 T ) k β k +D2
wherein D2, D3, D4, D5 are all beta k Irrelevant part, then offset beta k Is a real root of the formula:
in addition, since the offset β has the same sparse structure as the source, P and V can be reduced in dimension to K or k×k dimensions. F' (β) in formula (7) k ) The obtained root is the offset under one iteration, and in each iteration process, the mean value, covariance matrix and the updated super-parameter alpha are needed to be calculated 0 Alpha, beta, and terminating the iteration condition to reach the maximum number i of iterations max or ||αi+1 -α i || 2 /||α i || 2 ＜τ。
Super parameter alpha 0 The updating process of alpha and offset beta is as follows:
(1) Inputting an initial value: β=0, ρ=0.01, c=d=1×10 -4 ,
(2) Obtaining an overcomplete dictionary phi after unitary transformation according to a formula (1), and obtaining a mean mu (t) and a covariance sigma of a signal source according to formulas (2) and (3);
(3) The mean mu (t) and the covariance sigma are combined with the formula (4) and the formula (5) to obtain updated super-parameter alpha 0 Alpha, updating the deviation beta by using a formula (7);
(4) Judging whether the maximum iteration number i is reached max or ||αi+1 -α i || 2 /||α i || 2 If not, updating the unitary transformed overcomplete dictionary phi according to the formula (1) by using the updated offset beta, namely, turning to the step (1); if one or two conditions are met, ending the iteration and outputting DOA estimated values
wherein ,grid value, beta 'representing the jth signal source' j Is the grid offset for the jth signal source.
Next, description will be made with specific embodiments assuming that k=2 narrowband far-field signals are at an angle [ θ ] 1 ,θ 2 ,...θ K ] T Incident on a uniform linear array of m=8 omni-directional receive array elements. The wavelength of the incident signal is lambda, the distance between adjacent array elements is d=lambda/2,is distributed in [0, pi ]]The spatial angle discrete sampling value on the grid is divided into N, N=91 is set, and the iteration times i are set max =2000, margin parameter τ=10 -3 The specific parameters are shown in table 1:
table 1 system simulation parameters
Parameter name Parameter values
Array element number (M) 8
Array element interval (d) Lambda (wavelength)/2
Angular range 0°～180°
Angular interval (r) 2°
Number of sources (K) 2
FIG. 2 is an angular cross-sectional view of the OGSBI algorithm at both coherent and incoherent sources, as can be derived from FIG. 2, when the source is an incoherent source, the OGSBI algorithm can accurately estimate the signal orientation; when the signal source is a coherent source, the estimation performance is rapidly degraded.
Fig. 3 is an angular cross-section of a MUSIC algorithm estimating a coherent source before and after unitary transformation. As can be seen from fig. 3, after unitary transformation, the rank of covariance is recovered to rank (R) =k, the signal subspace and the noise subspace are correctly represented, and the MUSIC algorithm can estimate the coherent source with high accuracy, so as to provide a correct weighting vector.
The invention improves the OGSBI algorithm based on the unitary transformation of the guide vector second-order Taylor expansion grid-off model and the estimation model, wherein the OGSBI and the proposed algorithm IOGWSBI are shown in the spatial spectrum contrast diagram of the next Monte Carnot experiment at SNR=10dB in FIG. 4, and the corresponding results are shown in the table 2.
From fig. 4 and table 2, it can be seen that the estimation performance of IOGWSBI is significantly better than OGWSBI algorithm. This shows that the IOGWSBI algorithm can still maintain superior DOA estimation performance due to unitary transform decorrelation processing when the signal sources are coherent.
TABLE 2 DOA settlement results
θ 1 θ 2
true signal 64.8° 86.5°
OGWSBI 65.06° 87°
IOGWSBI 64.88° 86.55°
Fig. 5 is a plot of the DOA estimation root mean square error as a function of signal to noise ratio at a snapshot count l=100. Fig. 6 is a plot of the DOA estimation root mean square error as a function of snapshot number at snr=10 dB. As can be seen from fig. 5 and 6, both algorithms gradually decrease in root mean square error as the signal-to-noise ratio and the snapshot count increase. But the weighted vector is correctly represented due to the decorrelation process performed by the IOGWSBI algorithm. Therefore, the proposed algorithm is superior to the OGWSBI algorithm under the condition of equal signal-to-noise ratio or snapshot count, and the estimated performance is improved by about 50%.
The IOGWSBI algorithm consists of unitary transformation, singular value decomposition and weighted sparse reconstruction 3 parts. The unitary transformation computation is ignored because it involves only addition and subtraction operations. The computational complexity of the singular value decomposition is O (max (M2T, MT 2)). It can be found that both unitary transformation and singular value decomposition calculations need to be calculated only once, whereas the present algorithm is an iterative class algorithm, the algorithm complexity depends on the weighted sparse reconstruction part. The computation complexity of a single iteration of the OGSBI algorithm is O (max (MN 2)), and under a coherent information source, the iteration times are increased due to wrong weighting information, so that the computation complexity is further increased. The IOGWSBI uses unitary transformation, the operation of one real number domain is only 1/4 of the previous complex number domain, and the number of iterations is greatly reduced due to the correct weighting information. In addition, the IOGWSBI algorithm adopts a guide vector second-order Taylor expansion model, so that the operation complexity is improved to a certain extent compared with the first-order model, and the overall operation speed is still superior to that of the OGWSBI algorithm.
Fig. 7 is a graph of algorithm run time as a function of signal to noise ratio at a snapshot count l=100. As can be seen from fig. 7, when the signal-to-noise ratio is changed between 0dB and 20dB, the operation time of the two algorithms is continuously reduced as the signal-to-noise ratio is increased, and the operation efficiency of the IOGWSBI algorithm is improved by about 60% compared with that of the OGWSBI algorithm. Therefore, the IOGWSBI algorithm is an efficient and high-precision grid-off DOA estimation algorithm under the condition of a coherent information source, and is more suitable for scenes with higher requirements on precision.
According to the invention, on the basis of the OGSBI algorithm, through unitary transformation processing on the estimation model, not only can the incoherent processing be carried out on the coherent information source, and the problem of insufficient estimation performance of the OGSBI algorithm under the coherent information source is solved, but also the algorithm can be converted from a complex domain to a real number domain for operation, and the operation efficiency of the algorithm is remarkably improved. In addition, in order to further improve the estimation precision, the second-order taylor expansion is also performed on the basis of the first-order taylor expansion of the guide vector, so that the fitting error of the signal is reduced. The algorithm provided by the invention is effectively improved in precision and efficiency, and the actual application scene of the weighted sparse Bayesian algorithm is widened.
The foregoing is merely illustrative of specific embodiments of the present invention and no limitations are intended to the scope of the invention, as defined in the appended claims.

Claims (7)

1. A coherent source grid-off DOA estimation method based on weighted second-order sparse Bayes is characterized in that the DOA estimation method is used for the following models: the received signal isThe sparse expression is Y c =Φ (β) s+n, where +.>Is a signal source, beta is an angle deviation amount, +.>Representing noise, wherein M is the number of array elements, N is the number of grid divisions, T is the number of snapshots, K is the number of signal sources, and phi is an overcomplete dictionary formed by guide vectors;
the DOA estimation method comprises the following steps:
step S1: for the received signal Y c The unitary transformation realizes real number domain transformation and signal decoherence processing, so that a received signal Y after the unitary transformation is obtained;
step S2: decomposing Y singular values of the received signal after unitary transformation to obtain Y sv S and S sv Constructing a weighting vector w by combining with a MUSIC algorithm;
step S3: solving super-parameter alpha by unitary transformation of parameter matrix of overcomplete dictionary constructed by second-order guide vector and combining weighted sparse Bayes inference 0 Alpha and offset beta, and outputs DOA estimatesMetering value
2. The method for estimating the coherent source-isolated DOA based on weighted second-order sparse Bayesian as set forth in claim 1, wherein the step S3 comprises the steps of:
step S31: an overcomplete dictionary is constructed by using a real source arrival angle guide vector of second-order Taylor expansion:
wherein ,Ac For an observation matrix:is distributed in [0, pi ]]The space angle on the grid is used for dispersing sampling values, and N is the grid dividing number; the steering vector for the second order taylor expansion is Is the angle theta with the real signal k Nearest grid value, +.>Is a (theta) is->First derivative of the place->Is a (theta) is->Second derivative of the location, by->The matrix is-> Matrix of components->
Step S32: for A in an overcomplete dictionary c 、B c C (C) c Performing unitary transformation to obtain overcomplete dictionary after unitary transformation
Step S33: by usingΛ＝diag(α)、p(α n )＝Γ(α|1,w n ρ) is a user-selected parameter and a signal source S sv Posterior probability distribution ∈> The mean and variance μ (t) =α of the signal are obtained 0 ∑Φ H y sv (t),t＝1,....K，∑＝(α 0 Φ H Φ+Λ -1 ) -1 Updating a mean μ (t) and a variance Σ of a signal using an overcomplete dictionary Φ after unitary transformation, and updating a super parameter α based on the mean μ (t) and the variance Σ of the signal 0 Alpha and offset beta; judging whether the maximum iteration number i is reached max or ||αi+1 -α i || 2 /||α i || 2 And if not, updating the over-complete dictionary phi by using the updated offset beta, and continuously updating the mean mu (t) and the variance sigma of the signals by using the updated over-complete dictionary phi so as to update the super-complete dictionary phiParameter alpha 0 Alpha and offset beta; if one or two conditions are satisfied, ending the iteration and outputting DOA estimate +.>
3. The coherent source-isolated DOA estimation method based on weighted second-order sparse Bayes as claimed in claim 2, wherein the updated hyper-parameters alpha are 0 Alpha is respectively as follows:
wherein μ= [ μ (1),. Mu.μ (K)]＝α 0 ∑Φ H Y sv ， ρ＝ρ/K，/>b,c→0。
4. The coherent source-isolated DOA estimation method based on weighted second-order sparse Bayes according to claim 3, wherein the updated offset beta is:
wherein ,
5. the method for estimating the coherent source-isolated DOA based on weighted second-order sparse Bayes according to claim 2, wherein the step S1 comprises the following steps:
step S11: for the received signal Y c Constructing an augmentation matrix to form a central hermite matrix:
wherein ,Yc * Is Y c Is used for the complex conjugate of (a),
step S12: to the center Hermite matrix Y aug Unitary transformation processing:
wherein Y represents Y aug After unitary transformation, transforming from complex domain to matrix of real number domain, U is unitary matrix;
when M is even, U M Can be expressed as:
wherein I is an identity matrix of M/2 xM/2, J is an exchange matrix of M/2 xM/2, the auxiliary diagonal line is 1, and the other elements are 0;
when M is odd number, U M Can be expressed as:
wherein the dimension of I and J is (M-1)/2;
similarly, U 2T Is a 2T dimensional unitary matrix.
6. The method for coherent source-isolated DOA estimation based on weighted second order sparse Bayes as claimed in claim 5, wherein step S32 is performed on A in an overcomplete dictionary c 、B c C (C) c A, B and C for unitary transformation are as follows:
。
7. the method for estimating the coherent source-isolated DOA based on weighted second-order sparse bayesian according to claim 2, wherein the step S2 comprises the steps of:
singular value decomposition of the unitary transformed received signal Y, i.e. y=u s ∑ s V s T +U e ∑ e V e T Obtaining a signal subspace U s Noise subspace U e The method comprises the steps of carrying out a first treatment on the surface of the Order the Obtaining Y for the real signal source sv 、S sv ；
The inverted MUSIC spatial spectrum formula is:weight w= [ w ] 1 ,…,w N ] T And simultaneously normalizing the weight values to obtain a weight vector w: w=w/min (w).
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